Combining (2) and (3) : K-f^^f{Z)dZ (4) 



Thus solve for K for each Bathythermogram. 



Without regard as to which Bathythermogram represents the true heat content 

 of the ocean, each Bathythermogram in the series can be compared to some arbitrary 

 reference heat content. Having established a quantity vi^hich must be added or sub- 

 tracted from each individual Bathythermogram in order to make the heat content 

 equal, this quantity can be re-translated into terms of a AT. This AT is the correction 

 factor M^hich should be applied to the Bathythermogram to cause the Bathythermo- 

 gram to register the same heat content. 



This technique cannot be applied to ocean conditions where considerable internal 

 waves are present. Internal waves will represent an actual change in heat content 

 of the ocean at that point from BT i eading to BT reading. This technique would 

 erroneously provide for a horizontal displacement of the Bathythermogram to over- 

 come a vertical displacement in the water. In cases where internal waves are present, 

 other techniques such as curve fitting techniques to be described below will have to 

 be employed. 



9.3.2. Curve Fitting Techniques 



Thus far the processes for comparing Bathythermograph data have involved 

 the use of their absolute grid values and various applied correction factors. A much 

 more accurate picture of variation in the ocean can be obtained if the determinate 

 errors of the instrument and the man-made determinate errors are first eliminated. 

 This can be accomplished if the individual Bathythermograms are compared, not 

 by their absolute grid values, but rather by superimposing one curve on top of an- 

 other and noting the variations between the curves. This is a method for correcting 

 the Bathythermograms; i.e., superimiposing the non-varying portions of the curves 

 upon each other. 



* 



This in actuality is correcting the temperatures at many depths rather than 

 trying to correct the Bathythermograph by one single temperature measurement at 

 the surface. The absolute value of the superimposed curve is still undetermined, but 

 nevertheless the ocean variability can be shown by comparing the variations of these 

 superimposed curves. 



The assumption involved in curve fitting techniques are that the areas which are 

 being investigated are relatively stable to begin with, and it is quite unlikely that the 

 ocean will change in displacement throughout the entire exploration of the BT unit. 

 It is considered then that the average deviation which is obtained by this type of 

 comparison comes closer to approximating the true ocean variation than comparing 

 BT's by their absolute values. 



Two techniques are available for fitting these curves. The simplest and perhaps 

 the most reliable is visual comparison. This is accomplished by superimposing 

 transparent Bathythermograph slides of a given series until the curves are matched 

 in their greater proportion. A grid can then be placed over top of these to determine 

 the magnitude of the variations between the two curves. Scale differences must 

 be considered. 



If is is desired, a rigid mathematical approach can be applied to the curve fitting 

 techniques. Several mathematical techniques have been suggested (refer to literature 

 survey at the end of this report) . It will require further study to determine the 

 practicality and desirability of applying mathematical techniques in lieu of visual 

 superimposition. 



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